how to apply the monte carlo (MC) method on my BPSK_TX_RX code?

I made this code and I would like some help to apply the Monte Carlo (MC) method in this programming.

Help me!!!

the code follows below:

% BPSK
M = 2;                 

% número de bits ou símbolos
N = 1000000;   

% transmissor

% Gera bits aleatórios ( matriz de variaveis binarias)
Bits_ale = randi([0 M-1],1,N);

% Modulação BPSK 0 -> -1; 1 -> 1
Bits_bpsk = 2 * Bits_ale-1;        

% Gera bits de marca d'água aleatórios
Bit_wat = randi([0 M-1],1,N);

Theta = pi/8; 

b = 1/sqrt(2)*(randn(1,N) + 1i*randn(1,N)); % white gaussian noise with 0dB variance 

Eb_N0_dB = 0:20; % multiple Eb/N0 values

for k = 1:N 

    
    if Bit_wat(k)==1
        
        Bit_enviado(k) = Bits_bpsk(k) * exp(1i * Bits_bpsk(k) * Theta);
        
    else
        
        Bit_enviado(k) = Bits_bpsk(k) * exp(-1i * Bits_bpsk(k) * Theta);
    
    end
    
end


for iter = 1:length(Eb_N0_dB)
  
    % Noise addition
   
    d = Bit_enviado + 10^(-Eb_N0_dB(iter)/20)*b; % additive white guassian noise
  
    % receiver - hard decision decoding
   
    ipHat = real(d)>0;
   
    % counting the errors
   
    nErr(iter) = size(find(Bits_ale- ipHat),2);
    
end

simBer = nErr/N; % simulated ber

theoryBer = 0.5*erfc(sqrt(10.^(Eb_N0_dB/10))); % theoretical ber

% plot
close all
figure
semilogy(Eb_N0_dB,theoryBer,'b.-');
hold on
semilogy(Eb_N0_dB,simBer,'mx-');
axis([0 10 10^-5 1])
grid on
legend('theory', 'simulation');
xlabel('Eb/No, dB');
ylabel('Bit Error Rate');
title('Bit error probability curve for BPSK modulation');
hold on
grid on

Answer 1

[Drishti]

Hi Adriane,

To implement Monte Carlo (MC) method, an outer loop for fixed number of ‘MonteCarloTrials’ can be applied over the provided code.

The outer loop on ‘MonteCarloTrails’ is used for the following reasons:

• For each trail, the MC method generates random bits and noise transmitted and received.
• At the end, for all the trails, error is averaged out for reliable estimation of ‘BER (Bit Error Rate)’.

Also, to store the errors for each value ‘nErr’ is utilized.

Refer to the implementation below for better understanding. The ‘nErr’ variable is used to store the errors for each iteration:

nErr = zeros(length(Eb_N0_dB), 1);
for trial = 1:MonteCarloTrials
    % Generate random bits (matrix of binary variables)
    Bits_ale = randi([0 M-1], 1, N);
    % BPSK modulation: 0 -> -1, 1 -> 1
    Bits_bpsk = 2 * Bits_ale - 1;
    % Generate random watermark bits
    Bit_wat = randi([0 M-1], 1, N);
    Theta = pi/8;  
    b = 1/sqrt(2)*(randn(1, N) + 1i*randn(1, N)); 
    % Preallocate transmitted bits
    Bit_enviado = zeros(1, N);
    % Apply watermark modulation
    for k = 1:N
        %similar to original code
    end
    % Loop over each Eb/N0 value
    for iter = 1:length(Eb_N0_dB)
        %similar to original code
    end
end
% Calculate the average error rate over all trials
simBer = nErr / (N * MonteCarloTrials);
% Theoretical BER for BPSK (without watermarking)
theoryBer = 0.5 * erfc(sqrt(10.^(Eb_N0_dB/10))); 

Refer to the attached output graph for reference.

I hope this works.